This work can be extended in several directions. It might for example not be clear when symptoms exactly start. Therefore, it might be possible that just a window for symptom onset can be supplied ([1]}). Moreover, it can be of interest to include asymptomatic patients by including a certain cure-probability, i.e. the probability with which patients will never show symptoms. As an alternative one could also consider follow up studies in which the symptom onset time of patients is considered as a censored variable (in which case asymptomatic patients can be interpreted as patients who show symptoms at \(\infty \) ). Finally, the dataset by [2]} includes also a window for infection of the second person. It would of course be interesting to include this information in the model. But we would like to point out that this is not entirely trivial because it is unclear how to model the time of infection within this window. As we motivated in the beginning of Section  a simple uniformity assumption is possibly difficult to justify. Therefore, we would suggest to include this distribution in the estimation in a suitable way. In theoretic terms, the most interesting question would certainly be to establish asymptotic normality results which allow the researcher to make quantitative statements. Such statements can for example be achieved by following the semi-parametric framework as e.g. in [3]}. Another interesting question would be how to adequately incorporate covariates in the model. It could be the case that e.g. younger and older people have different incubation periods or generation times.
